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It is almost customary in textbooks to speak of the "Kelvin-Planck statement" of the law, as for example in the text by ter Haar and Wergeland.

It is almost customary in textbooks to speak of the "Kelvin-Planck statement" of the law, as for example in the text by ter Haar and Wergeland.

教科书中几乎<font color = 'red'><s>惯常提及该定律的“'''<font color = '#ff8000'>开尔文-普朗克表述 Kelvin-Planck Statement</font>'''”</s></font><font color = 'blue'>总是用“'''<font color = '#ff8000'>开尔文-普朗克表述 Kelvin-Planck Statement</font>'''”来称呼该定律</font>，例如'''<font color = '#ff8000'>德克·特哈尔 Diek ter Haar</font>''' 和'''<font color = '#ff8000'>哈拉尔德·沃格兰 Harald Wergeland</font>''' <font color = 'red'><s>在文中</s></font>就是这样表述的。

教科书中几乎总是用“'''<font color = '#ff8000'>开尔文-普朗克表述 Kelvin-Planck Statement</font>'''”来称呼该定律，例如'''<font color = '#ff8000'>德克·特哈尔 Diek ter Haar</font>''' 和'''<font color = '#ff8000'>哈拉尔德·沃格兰 Harald Wergeland</font>''' 就是这样表述的。

Every process occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limit, i.e. for reversible processes, the sum of the entropies remains unchanged.

Every process occurring in nature proceeds in the sense in which the sum of the entropies of all bodies taking part in the process is increased. In the limit, i.e. for reversible processes, the sum of the entropies remains unchanged.

Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:

Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation. His statement of the second law is known as the Principle of Carathéodory, which may be formulated as follows:

'''<font color = '#ff8000'>康斯坦丁·卡拉西奥多里 Constantin Carathéodory</font>'''在纯数学公理的基础上进行了热力学<font color = '#ff8000'>公理化formulated</font><font color = 'blue'>阐明</font>。他对第二定律的陈述被称为'''<font color = '#ff8000'>卡拉西奥多里原理 Principle of Carathéodory</font>'''，可以这样表述:

'''<font color = '#ff8000'>康斯坦丁·卡拉西奥多里 Constantin Carathéodory</font>'''在纯数学公理的基础上进行了热力学<font color = '#ff8000'>公理化formulated阐明。他对第二定律的陈述被称为'''<font color = '#ff8000'>卡拉西奥多里原理 Principle of Carathéodory</font>'''，可以这样表述:

With this formulation, he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, <math>\delta Q=TdS</math>.  

With this formulation, he described the concept of adiabatic accessibility for the first time and provided the foundation for a new subfield of classical thermodynamics, often called geometrical thermodynamics. It follows from Carathéodory's principle that quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, <math>\delta Q=TdS</math>.  

<font color = 'red'><s>公理化处理后，</s></font><font color = 'blue'>通过这个阐明，</font>他<font color = 'red'><s>第一次</s></font><font color = 'blue'>首次</font>描述了'''<font color = '#ff8000'>绝热可达性 Adiabatic Accessibility</font>'''的概念，并成为经典热力学的一个新的子领域，即通常所说的'''<font color = '#ff8000'>几何热力学  Geometrical Thermodynamics</font>'''<font color = 'red'><s>奠定了基础</s></font>。由卡拉西奥多里原理可以推出，<font color = 'red'><s>准静态转移的热的值是一个可积过程函数，</s></font><font color = 'blue'>作为热的能量的准静态转移是一个'''<font color="#ff8000"> 完整的过程函数holonomic process function</font>'''</font>即<math>\delta Q=TdS</math>。

通过这个阐明，他首次描述了'''<font color = '#ff8000'>绝热可达性 Adiabatic Accessibility</font>'''的概念，并为经典热力学的一个新的子领域，即通常所说的'''<font color = '#ff8000'>几何热力学  Geometrical Thermodynamics</font>'''<font color = 'red'><s>奠定了基础</s></font>。由卡拉西奥多里原理可以推出，作为热的能量的准静态转移是一个'''<font color="#ff8000"> 完整的过程函数holonomic process function</font>'''即<math>\delta Q=TdS</math>。

  --[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）准静态转移的热量值是一个可积过程函数 存疑

  --[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）准静态转移的热量值是一个可积过程函数 存疑

  --[[用户:小头盔|小头盔]]（[[用户讨论:小头盔|讨论]]）这里建议标注一下'''<font color="#ff8000"> 完整的过程函数 holonomic process function</font>'''

  --[[用户:小头盔|小头盔]]（[[用户讨论:小头盔|讨论]]）这里建议标注一下'''<font color="#ff8000"> 完整的过程函数 holonomic process function</font>'''

 

Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.<ref name="Munster 45">Münster, A. (1970), p. 45.</ref>{{sfnp|Lieb|Yngvason|1999|p=49}}<ref name="Planck 1926">[[Max Planck|Planck, M.]] (1926).</ref><ref>Buchdahl, H.A. (1966), p. 69.</ref> {{clarify|date=February 2014}}

Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.<ref name="Munster 45">Münster, A. (1970), p. 45.</ref>{{sfnp|Lieb|Yngvason|1999|p=49}}<ref name="Planck 1926">[[Max Planck|Planck, M.]] (1926).</ref><ref>Buchdahl, H.A. (1966), p. 69.</ref> {{clarify|date=February 2014}}

Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.  

Though it is almost customary in textbooks to say that Carathéodory's principle expresses the second law and to treat it as equivalent to the Clausius or to the Kelvin-Planck statements, such is not the case. To get all the content of the second law, Carathéodory's principle needs to be supplemented by Planck's principle, that isochoric work always increases the internal energy of a closed system that was initially in its own internal thermodynamic equilibrium.  

尽管在教科书几乎惯称卡拉西奥多里原理<font color = 'red'><s>表述了第二定律</s></font><font color = 'blue'>也是第二定律的一种表述</font>，并认为其与克劳修斯表述或开尔文-普朗克表述等价，但事实并非如此。为了得到第二定律的所有内容，需要对卡拉西奥多里原理补充普朗克表述，即等量功总是增加一个最初处于自身内部热力学平衡的封闭系统的内部能量。

尽管在教科书几乎惯称卡拉西奥多里原理也是第二定律的一种表述，并认为其与克劳修斯表述或开尔文-普朗克表述等价，但事实并非如此。为了得到第二定律的所有内容，需要对卡拉西奥多里原理补充普朗克表述，即等量功总是增加一个最初处于自身内部热力学平衡的封闭系统的内部能量。

===Planck's principle 普朗克原理===

===Planck's principle 普朗克原理===

... there is only one way in which the entropy of a [closed] system can be decreased, and that is to transfer heat from the system.

... there is only one way in which the entropy of a [closed] system can be decreased, and that is to transfer heat from the system.

Carnot's theorem (1824) is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs. Carnot's theorem states:

Carnot's theorem (1824) is a principle that limits the maximum efficiency for any possible engine. The efficiency solely depends on the temperature difference between the hot and cold thermal reservoirs. Carnot's theorem states:

'''卡诺定理 Carnot's Theorem'''（1824）是一条限制任何可能的<font color = 'red'><s>发动机</s></font><font color = 'blue'>热机</font>的最大效率的原理。效率完全取决于<font color = 'red'><s>热库和冷库之间的温差</s></font><font color = 'blue'>热源中热和冷之间的温差</font>。 卡诺定理指出:

'''卡诺定理 Carnot's Theorem'''（1824）是一条限制任何可能的热机的最大效率的原理。效率完全取决于热源中热和冷之间的温差。 卡诺定理指出:

*All irreversible heat engines between two heat reservoirs are less efficient than a [[Carnot engine]] operating between the same reservoirs.

*All irreversible heat engines between two heat reservoirs are less efficient than a [[Carnot engine]] operating between the same reservoirs.

 

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as [[thermodynamic reversibility]]. Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realise the [[Carnot cycle]]'s reversibility and was condemned to be less efficient.

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as [[thermodynamic reversibility]]. Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realise the [[Carnot cycle]]'s reversibility and was condemned to be less efficient.

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realise the Carnot cycle's reversibility and was condemned to be less efficient.

In his ideal model, the heat of caloric converted into work could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. Carnot, however, further postulated that some caloric is lost, not being converted to mechanical work. Hence, no real heat engine could realise the Carnot cycle's reversibility and was condemned to be less efficient.

在他的理想模型中，<font color = 'red'><s>热转换成功</s></font><font color = 'blue'>热转化为功的过程</font>可以通过逆转循环的运动而恢复，这个概念后来被称为'''<font color = '#ff8000'>热力学可逆性 Thermodynamic Reversibility</font>'''。然而，卡诺进一步假定，一些热<s>量</s>损失了，并没有转化为机械功。因此，没有一个真实的热机能够实现'''<font color = '#ff8000'>卡诺循环 Carnot Cycle</font>'''的可逆性，并且被认为效率较低。

在他的理想模型中，热转化为功的过程可以通过逆转循环的运动而恢复，这个概念后来被称为'''<font color = '#ff8000'>热力学可逆性 Thermodynamic Reversibility</font>'''。然而，卡诺进一步假定，一些热<s>量</s>损失了，并没有转化为机械功。因此，没有一个真实的热机能够实现'''<font color = '#ff8000'>卡诺循环 Carnot Cycle</font>'''的可逆性，并且被认为效率较低。

The equality holds in the reversible case and the strict inequality holds in the irreversible case. The reversible case is used to introduce the state function entropy. This is because in cyclic processes the variation of a state function is zero from state functionality.

The equality holds in the reversible case and the strict inequality holds in the irreversible case. The reversible case is used to introduce the state function entropy. This is because in cyclic processes the variation of a state function is zero from state functionality.

等号在可逆情况下成立，严格不等号在不可逆情况下成立。可逆情况下引入状态函数熵。这是因为在循环过程中，<font color = 'red'><s>状态函数的变化为零。</s></font><font color = 'blue'>状态功能的变化相对于状态功能为零。</font>

等号在可逆情况下成立，严格不等号在不可逆情况下成立。可逆情况下引入状态函数熵。'''<font color="#32CD32">这是因为在循环过程中，状态功能的变化相对于状态功能为零。This is because in cyclic processes the variation of a state function is zero from state functionality.</font>'''

   --[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）末句存疑

   --[[用户:Dorr|Dorr]]（[[用户讨论:Dorr|讨论]]）末句存疑

According to the Clausius equality, for a reversible process

According to the Clausius equality, for a reversible process